I have a question about who can receive payments from members that are not donations. Some examples would be the payment of girls camp fees, scout camp fees, etc.

I would suppose that these are governed by this same principal: "Only the bishop and his counselors may receive tithes and other offerings. Under no circumstances should their wives, other members of their families, clerks, or other ward members receive these contributions. The only exception is when Aaronic Priesthood holders are assigned to collect fast offerings."

That said, I have seen that it is often the practice for a YM leader to collect funds for camp, or for a YW leader to do the same.

Should these payments (they are not really donations or offerings per se) go to a member of the bishopric only? Or can they (unlike tithing and offerings) go to other people, who would then turn them in to the bishopric?

In a similar vein - the stake recently asked girls camp directors to bring the wards' camp payments (a check from the ward) to a meeting to turn in to the stake? (I don't know who from the stake would be there to collect it - not sure if that would be a member of the stake presidency, or a camp leader). Does this principal apply here? Is it ok to send the camp check with the camp leader? Is it ok for the camp leader to give the check to someone other than a member of the stake presidency?

Just because a procedure is "often the practice" doesn't make it right. You had it right the first time when you quoted the principle that only bishopric (or stake presidency) members may receive funds. There are excellent reasons for that policy.

Personally, I don't understand why people are afraid of using the mail for sending checks. I've seen people go to a lot of hassle and spend quite a bit more money on gas, seemingly just to avoid putting a stamp on an envelope addressed to the bishop or stake president.

Our assistant area auditor has made a particular point of making sure that funds are handled only by appropriate priesthood leaders (with the specific exception of fast offerings). I agree.

Even when a donation isn't considered "charitable" for tax purposes it's still a donation. The reason the policy works (the one that says only the Bishopric can accept donations) is that there is a system in place to process them. Any Bishopric member should have good habits to handle donations, whether they're received on a Sunday or another day. They won't misplace a donation before it's deposited or leave it in an unsafe location at home or in their car. When donations are received by a person who is not in the habit of receiving them there is great potential for something to go wrong, whether by accident or not. Also, when donations for camps are collected by a youth leader then the youth leader usually keeps track of who paid and how much. Then whatever is entered in MLS only shows a total without tracking individual donors' contributions. It's much better to handle these the same way you would any charitable donation and let MLS keep the record of exactly who paid, how much they paid and which category received it.